CNC Machine tool selection using MCDM techniques and application ...

International Journal of Engineering Trends and Technology (IJETT) – Volume 35 Number 7- May 2016

CNC Machine tool selection using MCDM techniques and application of software SANNA Vipul Gupta1, Babalu kumar2, Dr.Uttam Kumar Mandal 3 1

Graduate, Department of production Engineering, National Institute of Technology, Agartala Graduate, Department of production Engineering, National Institute of Technology, Agartala 3 Assistant Professor, Department of production Engineering, National Institute of Technology, Agartala 2

Abstract: Machine tool selection is a very complex procedure. It involves deep analysis of various factors affecting functioning and performance. CNC machine tool selection is also a such kind of problem[5]. Objective of this study is to perform various MCDM methods for selecting most appropriate machine tool. AHP method is used to calculate the weights of various criteria[10] . The numerical problem considered for MCDM application is related to CNC machine manufactured by leading companies of the world. Various criteria are well examined and weightage is assigned to each criteria on this basis. There are used three normal MCDM methods viz. TOPSIS , MOORA, COPRAS and one outranking method namely ELECTRE I. Weights obtained by AHP method are used for all successive applications .MS-Excel add-in application SANNA (System for ANalysis of Alternatives) is used for evaluation through TOPSIS and ELECTRE methods. Results demonstrate an effective method for selecting CNC machine tool. Analysis of complexity is carried out for each method to arrive on best method along with the best alternative. Keywords— CNC Machine tool, MCDM, SANNA, MOORA, TOPSIS, ELECTREI, COPRAS I. INTRODUCTION Decision making is very important part of any manufacturing firm in all fields. In today’s world of advanced technology, CNC machines are mainly used due to its inherent qualities of high accuracy and automation. Due to highly advanced features of CNC machine tools[4], there cost is also very high. It is need of any organization to select best alternative of CNC machine tool available in market to increase efficiency and cost effectiveness. Aptness of different machine tool depends upon purpose of application, hence there is needed an approach which quantifies this purpose in form of numerical data. MCDM methods are very effective

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decision making technique used in various organizations. In MCDM methods objective is divided into a set of alternatives and criteria. Various criteria possess different prominence on basis of which weights are assigned to each criteria and MCDM model is applied to arrive at selection of best alternative. Assigning of weightage requires profound knowledge of criteria and available alternatives, hence judgment made by experts bears huge importance. These judgments are given on basis of questionnaire prepared for the selected problem. SANNA is a MS-EXCEL add-in application used for applying MCDM technique on a given set of data. It is capable of handling MCDM problems having at most 50 criteria and 180 alternatives. There are various module provided in software like data, methods ,weights to accomplish the goal. Only a limited number of methods are listed in data base of this add-in application like TOPSIS, WSA, ELECTRE I, ELECTREIII , PROMETHEE. For the purpose of current study SANNA add-in application is used for applying ELECTRE I method. To accomplish CNC machine tool selection using MCDM [3] , seven criteria are selected[1] viz. Number of tools, Number of axes, Machine weight ,Horse power , Floor Layout, Maximum RPM and turning diameter[3]. Goal of current study is to select CNC machine tool for high product variety so all criteria are positive criteria except Floor layout and Machine weight which are kept minimum to ensure that machine occupy less space and is light in weight. AHP method is used to determine the weights of each criterion. TOPSIS, MOORA, COPRAS and ELECTRE I methods are applied for ranking of alternative. As a conclusion complexity of various methods are compared and best method is selected along with ranking of alternatives. Also the variation and similarities obtained in results are discussed.

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II. METHODOLOGY There are many management techniques available for machine tool selection. Accordingly different set of data is required. As far as CNC machine tool selection by MCDM technique is concerned procedure followed for current study may be adopted[6]. Leaflets of various companies are collected from online and offline sources[3] and relevant criteria along with alternatives are enlisted. AHP method by T.L.Saaty[12] is used for calculating weights of various criteria. Pairwise comparison matrix of various criteria is prepared and values are assigned according to Saaty’s scale. Value provided in pairwise comparison matrix is a result of questionnaire prepared for recording expert’s judgment. To check the consistency of judgment, Consistency Ratio (CR) is checked which must be less than 0.1 otherwise the questionnaire, expert’s opinion or both are changed. Once the weights of criteria are calculated, different MCDM methods are applied to get the rankings of alternatives. Calculations obtained in various methods and complexity associated helps in determining the best MCDM method for CNC machine tool selection problem. A block diagram of complete procedure is shown in Fig.1. Entire methodology is divided into four stages viz. S-I, S-II, S-III and S-IV. In beginning of first stage, type of production system is needed to be decided. Different production system requires varying weightage and optimization of criteria. For instance a production system based on product technology does not require enough variety hence CNC machine tool for such system is required to have high speed to process the material with less number of tools. In contrary to this job shop based production system requires CNC machine tool with more number of axes and tools to ensure product variety. Various CNC machine tools are available in market with varying cost and features. Data of these tools are provided in the leaflets provided along with machines or the website of companies[7]. For the purpose of current study data are collected with the reference of research paper [3].After creating database of various options main factors affecting selection procedure are enlisted known as criteria in MCDM calculations [9]. This completes the stage I.

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Stage II involves assigning weights to various criteria. This stage is vital as it includes the judgment scheme of experts to assign values to each criterion according to Saaty’s scale. Expert uses questionnaire already prepared for the problem and also their general intelligence. Brainstorming is also used for this purpose. Experts should be personals belonging to CNC manufacturing having expertise in both technical and managerial related concerns. Judgment made by experts is verified by checking consistency ratio, this completes stage II. Third stage includes mathematical formulation of data and its handling. Various MCDM methods are applied to acquire ranking of alternatives as per the data formulated in decision matrix. Analysis of results obtained is discussed in Stage IV to conclude complexity associated with each method and suitability to current case study. Fig.1 shows block diagram of whole procedure.

III. ILLUSTRATIVE CASE STUDY Current study comprises of CNC machine tool manufactured by four leading companies of world viz. NAKAMURA,DOSSAN,ROMI, MAZAK[3]. In accordance with the judgment of experts related to CNC & Previous literature work all the data related to four types of vertical CNC is collected along with their specification[3] which are treated as criteria[3] .The below mentioned criteria are considered : i. Diameter (Dia) ii. RPM iii. No. Of Tools (NOT) iv. No. Of Axes (NOA) v. Machine Weight (MW) vi. Floor Layout (FL) vii. Horse power (HP) Data are formulated in Table I as decision matrix along with the optimization of criteria

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Optimization

Max Diameter(in)

NAKAMURA

7.48

Table I: Decision Matrix Max Max Max RPM No. of No. of Tools Axes 5000 24 9

DOSSAN

9.5

6000

12

ROMI

11.02

6000

MAZAK

16.93

4000

Min Machine Weight(lbs) 26400

Min Floor Layout 1074.52

Max Horse power 15

8

16534

921.188

20

12

4

19000

2620.8

25

12

6

24250

1881.49

30

(A) Determination of weights by AHP(Analytical hierarchy process) Method: T.L. Saaty in 1980's developed method of pair wise comparison to determine weights of various criteria[8]. It is very useful method rapidly used for determining the weights[9]. Step I: Pair wise comparison according to Saaty’s nine-point scale Table II: Pair wise comparison Matrix Dia(in)

RPM

NOT

NOA

MW(lbs)

FL

HP

Dia(in)

1

0.5

1

1

2

1

0.5

RPM

2

1

2

2

2

2

0.5

NOT

1

0.5

1

1

2

1

0.5

NOA

1

0.5

1

1

2

1

0.5

MW

0.5

0.5

0.5

0.5

1

0.5

0.33

FL

1

0.5

1

1

2

1

0.33

HP

2

2

2

2

3

3

1

Step II. Normalization by Geometric mean:

i= No. of rows j= No. of columns n=No of rows/column or criteria.

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Table III : Normalized Matrix with priority vectors Dia(in)

RPM

NOT

NOA

MW(lbs)

FL

HP

GM

PV

Dia(in)

1

0.5

1

1

2

1

0.5

0.905

0.119

RPM

2

1

2

2

2

2

0.5

1.485

0.195

NOT

1

0.5

1

1

2

1

0.5

0.906

0.112

NOA

1

0.5

1

1

2

1

0.5

0.906

0.112

MW(lbs)

0.5

0.5

0.5

0.5

1

0.5

0.33

0.521

0.068

FL

1

0.5

1

1

2

1

0.33

0.855

0.112

HP

2

2

2

2

3

3

1

2.03

0.267

8.5

5.5

8.5

8.5

14

9.5

3.67

7.612

1

Step III. Consistency check: Consistency is checked by parameter known as Consistency Ratio(CR)

Where Eigen Value ,λ max = (8.5 0.119)+(5.5×0.195)+(8.5×0.112)+(8.5×0.112)+(14×0.068)+(9.5×0.112)+(3.67×0.267)=7.112 Consistency Index, CI = Consistency Ratio, CR =

=0.0186 =

As, CR < 0.1 , Comparison is consistent Hence the priority vectors obtained in last column of Table III are the corresponding weights of the criteria.

Fig2. Weights of various criteria

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(B) TOPSIS Method: TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) was developed by Hwang and Yoon in 1980 is considered as one of its most commonly accepted variants[11]. The basic concept of this method is that the selected alternative should have the shortest distance from the ideal solution and the farthest distance from the negative-ideal solution in some geometrical sense. SANNA add-in supports TOPSIS method hence can be evaluated using it[2].

Fig.3 Decision matrix formulated in SANNA

Fig.4 Modified input data to consider non-benefit criteria

Fig.5 Normalized Decision matrix

Fig.6 Weighted Normalized Decision matrix and calculation of closeness coefficient

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Table IV: Ranking according to TOPSIS method CNC Machine NAKAMURA 0.45232

Rank 3

DOSSAN

0.57841

1

ROMI

0.43095

4

MAZAK

0.55194

2

(C) MULTI OBJECTIVE OPTIMIZATION ON THE BASIS OF RATIO ANALYSIS (MOORA) METHOD: Multi objective optimization (or programming) is also known as multi criteria / multi attribute optimization, is the process of concurrently optimizing two or more disagreeing attributes(objective) subjected to certain constrain[14]. MOORA method, first introduced by Brauers (2004) is such a multi objective optimization technique that can be successfully applied to solve various types of complex decision making problems in the manufacturing environment. MOORA method starts with a decision matrix showing the performance of different alternatives with respect to various attributes (objectives). MOORA method is incompatible with SANNA add-in so elaborative calculation is carried out. Step I. Develop the initial decision matrix, X shown

Step II. Normalization of decision matrix is done by dividing each element of decision matrix with the square root of the sum of squares of each alternative per attribute which is represented as: [For i= 1,2,3 . . . . . .. .. . . . n] Step III. For multi-objective optimization, these normalized performances are added in case of maximization (for beneficial attributes) and subtracted in case of minimization (for non-beneficial attributes)[14].Then the optimization problem is shown in equation-

Step IV. To provide weightage to each attribute, it is multiplied with corresponding weight, equation becomes as follows:

Here,

is the weight of the

ℎ

criteria

The i value is determined by summation of corresponding element of maximum (benefit criteria) and minimum (non-benefit criteria) in weighted Normalized Decision Matrix for given alternative. Hence ranking is obtained with ranking in increasing order of yi Table V: Weighted Normalized Decision Matrix Weights 0.119 0.195 0.112 0.112 0.068 0.112 0.267 Criteria Dia(in) RPM NOT NOA MW(lbs) FL HP NAKAMURA 0.0381 0.0940 0.0907 0.0769 0.0409 0.0335 0.0863 DOSSAN

0.0484

0.1128

0.0453

0.0683

0.0257

0.0287

0.1151

ROMI

0.0561

0.1128

0.0453

0.0341

0.0295

0.0818

0.1439

MAZAK

0.0863

0.0753

0.0454

0.0513

0.0376

0.0587

0.1727

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Table VI: Ranking obtained by MOORA Alternatives NAKAMURA

0.3116

Qi 0.9287

Ranking 3

DOSSAN

0.3355

1

1

ROMI

0.2809

0.8372

4

MAZAK

0.3350

0.9985

2

(D) COPRAS method : In 1996 researchers developed Complex Proportional Assessment method abbreviated as COPRAS. Final ranking in COPRAS method is obtained by following equation: ----------------------(1)

Where, S-min is value of minimum criteria attribute , S+j denotes maximum criteria attribute and Zj is value of final ranking of jth alternative. Step I. Normalized decision matrix is obtained by direct summation ratio technique

Table VII: Normalized Decision matrix Max Max Max RPM NOT NOA

Optimization Criteria

Max Dia(in)

Min MW(lbs)

Min FL

Max HP

NAKAMURA

0.1664

0.2380

0.4

0.3333

0.3063

0.1653

0.1666

DOSSAN

0.2114

0.2857

0.2

0.2962

0.1918

0.1417

0.2222

ROMI

0.2452

0.2857

0.2

0.1481

0.2204

0.4033

0.2777

MAZAK

0.3768

0.1904

0.2

0.2222

0.2813

0.2895

0.3333

Step II :.Weighted Normalized Decision Matrix:

Table VIII: Weighted Normalized Decision Matrix 0.195 0.112 0.112 0.068

Weight

0.119

0.112

0.267

Criteria

Dia(in)

RPM

NOT

NOA

MW(lbs)

FL

HP

NAKAMURA

0.0198

0.0464

0.0448

0.0373

0.0208

0.0185

0.0445

DOSSAN

0.0252

0.0557

0.0224

0.0331

0.0130

0.0159

0.0593

ROMI

0.0292

0.0557

0.0224

0.0166

0.0150

0.0452

0.0741

MAZAK

0.0448

0.0371

0.0224

0.0249

0.0191

0.0324

0.0890

Step III. Benefit and non- Benefit criteria matrix is formulated using following equation:

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Table IX:. Benefit and non-Benefit criteria matrix

NAKAMURA

0.1928

0.0394

25.4127

DOSSAN

0.1958

0.0289

34.5743

ROMI

0.1981

0.0602

16.6213

MAZAK

0.2183

0.0516

19.3938 =

=

0.18

96.0022

Step IV: For final ranking equation (1) is used Table X: Ranking according to COPRAS method Pi (%)

Rank

NAKAMURA

0.2405

91.6823

3

DOSSAN

0.2623

100.0000

1

ROMI

0.2348

89.4978

4

MAZAK

0.2572

98.0359

2

(E) ELECTRE I Method: ELECTRE is a part of multi-criteria decision analysis methods which originated in Europe in mid of 1960s. ELECTRE stands for: ELimination and Choice Expressing Reality. This method was proposed by Bernard Roy and his fellow at SEMA consultancy firm. There are many versions of ELECTRE method like ELECTRE I , ELECTRE II , ELECTRE IV. ELECTRE I is an outranking methods used for determining best alternative rather than ranking of alternatives[15]. Further versions of ELECTRE facilitates the user to determine rankings of alternatives. SANNA is compatible with only ELECTRE I and ELECTRE III but for the current study only ELECTRE I is used.

Fig. 7 Decision Matrix

Fig8. Modified input data to consider optimization of Decision Matrix

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Fig.9 Concordance Matrix

Fig.10 Discordance Matrix

Fig.11 Aggregate Dominance Matrix In above calculations by SANNA add-in, alternative marked with EFEKT denotes the best alternative and no rankings are obtained. DOSSAN is designated as most suitable option according to ELECTREI method. IV. DISCUSSION AND CONCLUSION There are number of MCDM methods available with varying applicability and simplicity. There is slight difference between the results obtained by different MCDM methods. Although the results obtained for current study are same, but there may be observed some deviation in the results obtained. Various MCDM methods are based on varying mathematical formulation so the data is handled in different ways in different methods[15]. For example MOORA method is based on the ratio analysis while TOPSIS is based on deviation from the positive ideal and negative ideal solution[16] . Hence the distance and ratio gives two different results. Some of the reasons due to which results obtained are different may be stated as: (i) Different aggregation procedures and different normalization procedures sometimes leads to the selection of different most acceptable alternatives [16]. (ii) At the same time, different relative weights of criteria, used in the decision making model, can also have a significant impact on the selection of most appropriate alternatives, as well

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as ranking orders. In this case of CNC machine tool selection weights are kept constant in all the methods and due to application of different methods, normalization process involved in each method is changed, but it does not made any changes in the ranking of CNC machines. Upon literature survey and related case studies it is found that results obtained by different MCDM methods may vary due to their mathematical formulation [16].Same case may result in varying rankings with different MCDM methods when other set of data is taken. Closer results are obtained if data is handled to higher decimal places. Vector normalization procedure is used in the case of TOPSIS method which is based on deviation from ideal positive and negative solution. Selection of alternative is completely dependent on this deviation known as Euclidian distance[16]. The process of normalization and aggregation involves conversion of cost criteria into benefit criteria . In MOORA method normalization procedure is based on vector normalization without conversion of cost criteria into benefit criteria[14]. Formula used for ranking purpose in MOORA method is

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developed in the manner to consider the cost and benefit criteria. Hence it can be concluded that different MCDM methods have different areas of application for example TOPSIS is suitable for the location selection while ELECTREI[13] is used for the purpose where a single alternative is needed to be determined. COPRAS method involves linear transformation for the purpose of normalization without the conversion of cost criteria into benefit criteria .It is very similar to MOORA method but the aggregation process used is more complex. If the suitability of MCDM methods in given case is considered, it depends upon following criteria: (i) Calculation involved in the method (ii) Method of normalization causes change of criteria or not? (iii) Ease of application of formula for ranking

(iv)

Software support available for performing more complex calculations.

MOORA method can be considered as most suitable for the given problem. Calculations involved in MOORA method is less as compared to other MCDM methods used in the problem. Results can be obtained in simple three steps after formulating weighted normalized decision matrix. Method of normalization in MOORA involves vector normalization process without using change of criteria providing it an additional benefit for practical use . Change of criteria causes ambiguity in final matrices , but in MOORA approach positive and negative criteria are handled separately without merging or changing into single criteria. Final formula used in raking of alternatives by MOORA method involves direct subtraction of elements obtained by transformations in positive and negative criteria respectively.

Table XI: Ranking according to all methods used in illustration TOPSIS MOORA COPRAS Rank1

DOSSAN

DOSSAN

DOSSAN

Rank2

MAZAK

MAZAK

MAZAK

Rank3

NAKAMURA

NAKAMURA

NAKAMURA

Rank4

ROMI

ROMI

ROMI

ELECTREI

DOSSAN

For the given illustration it can be concluded that DOSSAN is the best alternatives and ROMI is most unsuitable alternative. MOORA is the best method to determine order of preference and ELECTREI is most suitable method for determining a single appropriate alternative.

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[7] Mishra S., Prakash, Tiwari M.K., and Lashkari R.S., 2006, ―A fuzzy goal-programming model of machinetool selection and operation allocation problem in FMS: A quick converging simulated annealing-based approach‖, International Journal of Production Research, 44, 43-76. [8] Yurdalul M., 2004, ―AHP as a strategic decisionmaking tool to justify machine tool selection‖, Journal of Materials Processing Technology, 146, 365-376. [9] Ayağ Z., and Özdemir R.G., 2006, ―A fuzzy AHP approach to evaluating machine tool alternatives‖, Journal of Intelligent Manufacturing, 17, 179-190. [10] Durán O., and Aguilo J., 2008, ―Computer-aided machine-tool selection based on a fuzzy-AHP approach‖, Expert Systems with Applications, 34, 1787-1794. [11] Yurdalul M., and ĺç Y.T., 2009, ―Analysis of the benefit generated by using fuzzy numbers in a TOPSIS model developed for machine tool selection problems‖, Journal of Materials Processing Technology, 209, 310-317. [12] Saaty T.L., 1980, The Analytical Hierarchy Process, McGraw Hill, New York. [13] Ermitita and S. Hartati, ―ELECTRE methods in solving group decision support system bioinformatics

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on gene mutation detection simulation‖, vol3, no1 Feb 2011 [14] U.K. Mandal and B.Sarkar, ―Selection of best IMS under fuzzy MOORA conflicting MCDM environment‖, International Journal of Emerging Technology and Advanced Engineering,vol-2, 2012. [15] M.Velasquez and P. T. Hester, ―An Analysis of MultiCriteria Decision Making Methods‖ ,International Journal of Operations Research Vol. 10, No. 2, 56-66 (2013). [16] D.Stanujkic, B. Đorđević, and M. Đorđević, ―comparative analysis of some prominent mcdm methods: a case of ranking serbian banks‖, Serbian Journal of Management 8 (2) (2013) 213 – 241.

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[17] J.M.-Gómez, G. Guerrón, R. A. Narvaez C, ―Cookware material selection by multi-criteria decision making (MCDM) methods‖, International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 8- April 2016 [18] J. Martinez , R.A. Narvaez C(2016), ―Use of Multicriteria Decision Making (MCDM) Methods for Biomass Selection Aimed to Fischer Tropsch Processes‖, Volume 34 Number 6- April 2016, 226272.

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